Image display sheet

ABSTRACT

An object is to provide an image display sheet provided for position detection of an object to be observed so as to realize a smooth pseudo moving image. The image display sheet is provided for an object  3000  to be observed for position detection and constituted by laminating a lenticular sheet composed of arrangement of a plurality of cylindrical lenses and an image forming layer, and an image formed on the image forming layer from a convex shape side of the cylindrical lenses of the lenticular sheet is formed to be observable as virtual image provided with movement, or movement and deformation. A plurality of images for observing virtual images for displaying virtual images  104 A,  104 B in association with the cylindrical lenses are formed repeatedly on the image forming layer so as to correspond to the cylindrical lenses respectively one-on-one, an arrangement pitch length in a horizontal direction of the flat convex lenses and a pitch length in a horizontal direction of the image for observing virtual image differs in a range of not more than 10%, and an arrangement pitch length in a vertical direction of the flat convex lenses and a pitch length in a vertical direction of the image for observing virtual image differs in a range of not more than 10%, and the virtual image smoothly moving with respect to displacement of an angle θ at which the object  3000  is visually observed is thereby observed.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a National Stage of International Application No. PCT/JP2012/060746 filed Apr. 20, 2012, claiming priority based on Japanese Patent Application No. 2011-096476 filed Apr. 22, 2011, the contents of all of which are incorporated herein by reference in their entirety.

FIELD OF THE INVENTION

The present invention relates to an image display sheet, and more particularly, to an image display sheet, which is capable of detecting a position of an object to be observed with respect to a camera using a virtual image with movement based on a cylindrical lens or flat convex lens and an image.

BACKGROUND TECHNOLOGY

There is known a method of recognizing positional relationship between an object to be observed and a robot by photographing the object to be observed by the camera provided for a head portion or a hand of a robot and detecting the position of the object to be observed with respect to the camera, or the position of the camera with respect to the object to be observed. For example, there is provided a method for detecting such position by photographing a rod-shaped projection provided for the object to be observed by a camera provided for the robot and then analyzing an image of the projection in the photographed image. In addition, there is also provided a method of analyzing the position of the robot using an infrared sensor.

In the meantime, there is provided an image display sheet in which an image can be observed as a virtual image such as moving, changing and like with movement, or movement and deformation by utilizing visual sense of an observer. The image display sheet is composed of a lenticular sheet which is constituted by an arrangement of a plurality of cylindrical lenses and an image forming layer.

FIGS. 26A and 26B are views for explaining a conventionally known image display sheet, in which FIG. 26A is a perspective view explaining a basic characteristic of a lenticular, and FIG. 26B is an illustrated view for explaining a basic principle of the lenticular.

A lenticular sheet 5001 is composed of cylindrical lenses 5002 and an image forming layer 5003 disposed on a surface opposite to a surface formed so as to provide a convex shape so that an image can be observed from a lens side in a pseudo moving manner. In an arrangement in shape of stripe of divided image 5004A to 5004D, a changing image in which an image is observed as if it changes by changing a stereoscopic image or viewing angles of the observer (right eye and left eye of the observer 5006 and 5007).

FIG. 27 is for explaining a conventionally known image display sheet 5009, in which (A) is a view for explaining a section of a conventionally known image sheet 5009, and (B) is a plan view of the image forming layer 5003. On the image forming layer 5003 formed to an image forming medium 5008, a plurality of original picture A, B, C, D are divided into stripe shape. FIG. 27 is an example in which the image for right eye 5004 and the image for left eye 5005 are divided each at predetermined width with respect to the respective lenses. When moving a line of sight (visual line of an observer), an A-image is observed at a certain position, a B-image is observed at another certain position, a C-image is observed at a further certain position, and a D-image is observed at a further certain position, as if the image is moved by changing the viewing (observing) angles of an observer.

Further, the Patent Document 1 discloses a technology in which when a plurality of original images are divided into stripe shape to form one sheet of images so as to create images which are observed as if they have different pictures as viewed from different viewing angles, boundary of a pitch of a convex lens and divided boundary of the image is made coincident with each other.

In the meantime, the Patent Document 2 discloses a technology in which an image for right eye of an observer and an image for left eye of the observer are divided into strip-shaped pieces each having a predetermined width with respect to each lens, and then, by arranging the divided pieces in interlace shape, a pseudo variable image is observed.

PRIOR ART DOCUMENT Patent Document

Patent Document 1: Japanese Patent Laid-open Publication No. 2003-344807

Patent Document 2: Japanese Patent Laid-open Publication No. 2010-044213

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

In a method in which it is required to detect a position of an object to be observed by providing a projection to the object to be observed, there is a problem such that position detecting performance decreases at a position in the vicinity of a front surface of the projection. Although such performance can be improved by using a long projection or fine projection, the long projection may obstruct an operation of a robot and the fine projection requires increased space of the location of such fine projection. In addition, since the projection has a weight itself, it is not available in a case when the projection is used for a long time by, for example, bonding it to a wall surface, which further requires several times of maintenance, thus being inconvenient and troublesome. Furthermore, since the projection requires some space for location, which will obstacle the operation or working, and in an adverse case, such as colliding to the projection, it may be broken or some accidents may be caused. Moreover, in a case of position detection using an infrared sensor, an infrared system is expensive, requiring much cost, thus also providing a problem.

Incidentally, as a visual effect such as moving or changing using a lenticular is an observation of a single image with in an observational perspective of a constant range and an observation of a next image exceeding the constant range by varying the observational perspective angle. As mentioned above, according to the variation (changing) of the observing angles, different images are sequentially observed.

At this time, the images observed sequentially according to the changing of the observing angles design an appropriate animated expression with action, magnification, reduction deformation of human, animal or like, and in such case, an visual effect such as if a motion picture is obtainable.

In an image display sheet in a conventional technology, a virtual image of an eye can be observed. However, as the line of sight is changed by changing the viewing angles, the images are observed as if frame-by-frame advance. Thus, such images are not taken as smooth motion for an observer, and in a certain case, virtual images are observed intermittently, which will give a sense of discomfort to the observer, thus being inconvenient.

An object of the present invention in consideration of the circumstances encountered in the conventional technologies mentioned above, is to provide image display sheet capable of realizing smooth pseudo moving image and capable of requiring no additional maintenance if once set, with thin and light shape as well as cheap cost.

Means for Solving the Problem

An image display sheet according to the present invention is provided for an object to be observed for position detection and constituted by laminating a lenticular sheet composed of arrangement of a plurality of cylindrical lenses and an image forming layer, and an image formed on the image forming layer from a convex shape side of the cylindrical lenses of the lenticular sheet is formed to be observable as virtual image provided with movement, or movement and deformation, wherein the lenticular sheet has a predetermined thickness so that the image forming layer is positioned on a focal surface of the cylindrical lenses, a plurality of images for observing virtual images for displaying single or a plurality of the virtual image in association with the cylindrical lenses are formed repeatedly on the image forming layer so as to correspond to the cylindrical lenses respectively one-on-one, an arrangement pitch length of the cylindrical lenses and a pitch length of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 10% , the image for observing the virtual image is an image reduced in size in the arrangement directions of the cylindrical lens of the virtual image as an object to be observed and the image for observing the virtual image, and the virtual image smoothly moving with respect to displacement of an angle at which the object is visually observed is thereby observed.

An image display sheet according to the present invention is provided for an object to be observed for position detection and constituted by laminating a flat convex lens sheet composed of arrangement of a plurality of flat convex lenses and an image forming layer, and an image formed on the image forming layer from a convex shape side of the flat convex lenses of the flat convex lens sheet is formed to be observable as virtual image provided with movement, or movement and deformation, wherein the flat convex lens sheet has a predetermined thickness so that the image forming layer is positioned on a focal surface of the flat convex lenses, a plurality of images for observing virtual images for displaying single or a plurality of the virtual image in association with the flat convex lenses is formed repeatedly on the image forming layer so as to correspond to the flat convex lenses respectively one-on-one, an arrangement pitch length in a horizontal direction of the flat convex lenses and a pitch length in a horizontal direction of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 5% and an arrangement pitch length in a vertical direction of the flat convex lenses and a pitch length in a vertical direction of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 5%, and the virtual image smoothly moving with respect to displacement of an angle at which the object is visually observed is thereby observed.

The image display sheet may be provided with a reference guide that is observable from a side having convex shape of the cylindrical lens or a side having convex shape of the flat convex lens.

It may be preferred that a plurality, not less than two kinds, of images for observing the virtual images having different pitch lengths are formed on the image forming layer repeatedly substantially one-on-one with respect to the cylindrical lenses or flat convex lenses, and a plurality of virtual images having at least one characteristic of different moving amount or different moving direction with respect to the displacement of an angle at which the object is visually observable is observable.

It may be preferred that a plurality, not less than two kinds, of images for observing the virtual images having different shapes or colors are formed on the image forming layer repeatedly substantially one-on-one with respect to the cylindrical lenses or flat convex lenses, and a plurality of virtual images having at least one characteristic of different shape and different color is observable.

Effect of the Invention

According to the image display sheets for position detection of the present invention, a pseudo moving image capable of being smoothly movable is realized, and the image display sheets capable of reducing feeling of strangeness is also realized.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of an image display sheet according to an embodiment of the present invention.

FIG. 2 is an illustration for explaining structure of the image display sheet according to the present embodiment, in which (A) is an explanatory view of a section of a lenticular sheet, and (B) is a plan view of an image forming layer.

FIG. 3 is a plan view of the image display sheet according to the present embodiment.

FIG. 4 is an explanatory view of a virtual image according to the present embodiment.

FIG. 5 is an illustration for explaining structure of the image display sheet according to another embodiment 1.

FIG. 6 is an illustration for explaining a pitch length measurement of an image 6 b.

FIG. 7 is an explanatory view of a virtual image according to another embodiment 1.

FIG. 8 is a sectional view of an image display sheet according to a further another embodiment 2.

FIG. 9 is an explanatory view for explaining structure of an image display sheet according to a further another embodiment 3.

FIG. 10 is a plan view of an image forming layer.

FIG. 11 is a sectional view of an image display sheet according to a further another embodiment 4.

FIG. 12A is an explanatory view for explaining structure of an image display sheet according to the further another embodiment 4.

FIG. 12B is a plan view of an image forming layer.

FIG. 13 is an explanatory view of a virtual image according to the further another embodiment 4.

FIG. 14 is an explanatory view of a virtual image according to the further another embodiment 4.

FIG. 15 is a plan view of an image forming layer of an image display sheet according to a further another embodiment 5.

FIG. 16A is a plan view of an image forming layer of an image display sheet according to a further another embodiment 6.

FIG. 16B is a plan view of an image forming layer of an image display sheet according to the further another embodiment 6.

FIG. 17 is an explanatory view for explaining structure of an image display sheet according to the further another embodiment 7.

FIG. 18 is an illustrated sectional view of an essential portion representing a focusing process to a lenticular sheet.

FIG. 19A is an explanatory view for explaining structure of an image display sheet according to a further another embodiment 8.

FIG. 19B is a view explaining an original image 113Xa and an original image 113Xb.

FIG. 19C shows a preparation example of an image group for observing still (stationary) virtual images.

FIG. 19D shows a preparation example of an image group for observing still virtual images.

FIG. 19E is an illustration for explaining a pitch length measurement of an image 113 b.

FIG. 20 is an explanatory view for explaining structure of a virtual image according to a further another embodiment 8.

FIG. 21 is an explanatory view of application example according to the further another embodiment 8.

FIG. 22A is a schematic view showing a position detection system S1 to which an image display sheet according to the present invention is used.

FIG. 22B is a sectional view of an image display sheet 1000.

FIG. 23A is an explanatory view of a camera position and a photographed image.

FIG. 23B is an explanatory view of a camera position and a photographed image.

FIG. 23C is an explanatory view of a camera position and a photographed image.

FIG. 23D is an explanatory view of a camera position and a photographed image.

FIG. 24A is an example of a photographed image.

FIG. 24B is an example of a photographed image using an image display sheet having another structure.

FIG. 24C is an example of a photographed image using an image display sheet having another structure.

FIG. 24D is an example of an image display sheet having reference guide.

FIG. 24E is an example of an image display sheet having reference guide.

FIG. 25A is a schematic view showing a position detection system S2 to which an image display sheet according to the present invention is used.

FIG. 26A is a view explaining a basic characteristic feature of a lenticular.

FIG. 26B is a schematic explanatory view for explaining a basic principle of the lenticular.

FIG. 27 is a view explaining an image display layer forming a conventionally known image display sheet.

MODE FOR EMBODYING THE INVENTION

An image display sheet according to the present invention will be described hereunder with reference to the accompanying drawings. The description will be made in detail as to various embodiments of an image display sheet which is provided to an object to be detected in position (described hereinlater).

FIG. 1 is a sectional view showing an image display sheet according to an embodiment of the present invention.

An image display sheet 100 is composed of a lenticular sheet 1 and an image forming layer 3 as essential elements. In this embodiment, an example in which the image forming layer 3 is formed to an image forming medium such as paper will be explained. Respective layers for constituting the image display sheet 100 will be explained.

The lenticular sheet 1 is composed of a plurality of cylindrical lenses 1 a, 1 a, - - - , 1 a that are arranged in parallel side by side. In the illustration of FIG. 1, the cylindrical lenses 1 a constituting the lenticular sheet 1 are positioned on an upper side. Although a material forming the lenticular sheet 1 is not limited to a specific one as far as a material has been conventionally used for an image display sheet, a transparent resin material such as PET (polyethylene terephthalate), PP, PETG (grico denatured polyethylene terephthalate), acryl, acrylate group resin or like.

The image forming medium 2 is provided for the lenticular sheet 1 on a side opposite to the side on which the cylindrical lenses 1 a having convex shape are not provided, and the image forming layer 3 is provided on the side of the lenticular sheet 1.

Although a material of the image forming medium 2 is not specifically limited as far as a material which has been conventionally used is used, paper, as a material of the image forming medium, such as coat (or coated) paper, synthetic paper, high quality paper, intermediate quality paper, impregnated paper, laminate (or laminated) paper, metal deposition paper, coated paper for printing, coated paper for recording or like will be used, and also, as a material of the image forming medium, polyethylene terephthalate film, polyethylene film, polypropylene film polycarbonate film or metal fail, or composite material thereof will be used. The material of the image forming medium 2 may be appropriately selected in accordance with required strength, usage or like as occasion demands.

The image forming layer 3 is a layer on which images 3 a such as pictures, letters or like as images for virtual image observation is printed or transferred. The image forming layer 3 is provided on the side of the lenticular sheet 1 of the image forming medium 2. Although a material of the image forming layer 3 is not specifically limited, as far as the material is adhesive to the image forming medium 2, for example, material for ink, and such material for ink may include light storage ink or fluorescent ink.

Further, as the method of laminating the lenticular sheet 1 and the image forming medium 2 to which the image forming layer 3, there may be performed by utilizing known adhesion and/or sticking method based on materials of the image forming medium 2 and the image forming layer 3 as far as the laminated layer of the lenticular sheet 1 and the image forming layer 3 remain transparency. That is, it may be adopted that an observer (eye E of the observer) can observe the image 3 a formed to the image forming layer 3 from the convex-shape side of the cylindrical lenses of the lenticular sheet 1. More specifically, it may be adopted that a virtual image in accordance with movement, or movement and deformation based on the image 3 a formed to the image forming layer 3 can be observed. Furthermore, the image forming layer 3 may be formed directly on a surface opposite to the surface on which the cylindrical lens 1 a of the lenticular sheet 1 is provided, the detail of which will be explained hereinafter with reference to FIG. 8.

FIG. 2 includes views for explaining structure or configuration of the image display sheet according to the present embodiment, in which FIG. 2(A) is a sectional view of the lenticular sheet, and FIG. 2(B) is a plan view of the image forming layer. FIG. 3 is a plan view of the image display sheet according to the present embodiment.

The example shown in FIG. 1 and FIG. 2(A) show a focusing condition of the respective cylindrical lenses 1 a in a case where the observer views the cylindrical lenses 1 a from a direction directly above the same at a time when the line of sight of the observer is moved by changing viewing angle of the observer in a direction of a white arrow. Further, in this case, focusing surface of the cylindrical lenses 1 a exists on the image forming layer 3. In other words, the cylindrical lenses 1 a are composed so that their focuses are concentrated on the image 3 a. Further, in actual, the observer can confirm the smooth movement, or movement and deformation of the virtual image by changing the viewing angle as well as viewing from a direction directly above the image 3 a.

As shown in FIG. 2(B), a plurality of images 3 a are formed on the image forming layer 3. In the examples shown in FIGS. 2(A) and 2(B), the images 3 a are formed repeatedly so as to correspond to the cylindrical lenses 1 a, respectively, one-on-one, that is, the images 3 a of six eyes correspond to the cylindrical lenses 1 a, respectively.

An image display sheet is constructed so that a difference between a pitch length A of arrangement of the adjacent cylindrical lenses 1 a and a pitch length B of the adjacent images 3 a satisfies that the difference is within a range of 0% to 10% with respect to the pitch length A of the cylindrical lenses 1 a or the pitch length B of the images 3 a.

In the example of FIG. 2, the image display sheet is constructed so that the arrangement pitch length A of the adjacent cylindrical lenses 1 a and the pitch length B of the adjacent images 3 a are different from each other and so that the difference between the pitch lengths A and B is not more than 10%.

In the case the pitch length B of the images 3 a is not more than the arrangement pitch length of the cylindrical lenses 1 a (A>B), the virtual image 4 based on the cylindrical lenses 1 a and the images 3 a will be observed stereoscopically for the observer in a manner such that the virtual image 4 goes down below the lenticular sheet 1. In this case, when the line of sight of the observer is moved rightward, the virtual image 4 is also observed as is moved rightward, and on the other hand, when the line of sight of the observer is moved leftward, the virtual image 4 is also observed as is moved leftward. That is, the virtual image 4 is observed in the same direction as the moving direction of the line of sight of the observer.

On the other hand, in the case the pitch length B of the images 3 a is not less than the arrangement pitch length of the cylindrical lenses 1 a (A<B), the virtual image 4 based on the cylindrical lenses 1 a and the images 3 a will be observed stereoscopically for the observer in a manner such that the virtual image 4 goes up (floats) above the lenticular sheet 1. In this case, when the line of sight of the observer is moved rightward, the virtual image 4 is observed as is moved leftward, and on the other hand, when the line of sight of the observer is moved leftward, the virtual image 4 is observed as is moved rightward. That is, the virtual image 4 is observed in the direction reverse to the moving direction of the line of sight of the observer.

A pitch length “x” of the virtual image 4 shown in FIG. 3 is determined by the following equation (1). A width “y” of the virtual image 4 in the arrangement direction of the cylindrical lenses 1 a is determined by the following equation (2). The character “A” is the pitch length of the arrangement of the cylindrical lenses 1 a, the character “B” is the pitch length of the images 3 a, the character “C” is a width (lateral size) of the image 3 a in the direction of the arrangement of the cylindrical lenses 1 a. In addition, height “z” (vertical size) of the image 3 a in the direction vertical to the arrangement direction of the cylindrical lenses 1 a is the same as a height “D” (vertical size) of the image 3 a in the direction vertical to the arrangement direction of the cylindrical lenses 1 a (equation (3)).

$\begin{matrix} \lbrack{Equations}\rbrack & \; \\ {x = \frac{A^{2}}{{A - B}}} & {{equation}\mspace{14mu}(1)} \\ {y = \frac{A \times C}{{A - B}}} & {{equation}\mspace{14mu}(2)} \\ {z = D} & {{equation}\mspace{14mu}(3)} \end{matrix}$

As mentioned above, the size of the virtual image 4 observed by the above equations (1) to (3) can be freely set by appropriately adjusting or changing the pitch length A of the arrangement of the cylindrical lenses 1 a, the pitch length B of the images 3 a, the width C of the image 3 a in the direction of the arrangement of the cylindrical lenses 1 a, and the height “D” of the image 3 a.

FIG. 4 is a view explaining the virtual image according to the present embodiment. As the observer moves while changing his line of sight by changing the viewing angle, the virtual images based on the images 3 a formed on the image forming layer 3 and the virtual images 4 based on the images 3 a formed on the image forming layer 3 and the cylindrical lenses 1 a are observed.

More specifically, in the case the pitch length B of the images 3 a is not more than the arrangement pitch length of the cylindrical lenses 1 a (A>B), the virtual image 4 based on the cylindrical lenses 1 a and the images 3 a will be observed stereoscopically for the observer in a manner such that the virtual image 4 goes down below the lenticular sheet 1. In addition, following the movement of the line of sight of the observer, the virtual image 4 can be observed as a virtual image moving smoothly.

On the other hand, in the case when the pitch length B of the images 3 a is not less than the arrangement pitch length of the cylindrical lenses 1 a (A<B), the virtual image 4 based on the cylindrical lenses 1 a and the images 3 a will be observed stereoscopically for the observer in a manner such that the virtual image 4 goes up above the lenticular sheet 1. In addition, following the movement of the line of sight of the observer, the virtual image 4 can be observed as a virtual image moving smoothly.

In the equations (1) and (2), while the value |A−B| becomes smaller, moving speed with respect to the movement of the line of sight becomes faster. Therefore, it is preferred that the value |A−B| is determined in accordance with the use condition of the image display sheet 100, that is, in view of speed of the movement of the line of sight of the actual observer. In other words, it is preferred that the moving speed of the virtual image 4 is set so as to accord with the speed of the line of sight of the observer.

According to the present embodiment, a plurality of images 3 a for displaying the virtual images in relation to the cylindrical lenses 1 a are formed on the image forming layer 3 in a repeated manner so as to correspond to the cylindrical lenses 1 a of the lenticular sheet 1, respectively, one-on-one. In addition, the images 3 a are formed such that the arrangement pitch length A of the cylindrical lenses 1 a and the pitch length B of the images 3 a differ from each other, and the difference between these pitch lengths A and B is not more than 10% with respect to the arrangement pitch length A of the cylindrical lenses 1 a or the pitch length B of the images 3 a. Accordingly, as a result, the image display sheet capable of observing the virtual images 4 with smooth movement, or movement and deformation can be realized. In addition, since the image size (width C and height D) of the image 3 a are approximately several tens μm to several tens mm, the image forming layer 3 can be printed and/or transferred to the image forming medium 2 by using a general equipment (for example, general-purpose printing machine, transferring machine, general-purpose image software and the like) without using dedicated equipment.

In a case where the lenticular sheet 1 having the arrangement pitch length A of the cylindrical lenses 1 a is in a range of 330 μm to 345 μm is used, it is preferred that the difference between the arrangement pitch length A of the cylindrical lenses 1 a and the pitch length B of the images 3 a differs, by 0.1% to 4%, with respect to the arrangement pitch length A of the cylindrical lenses 1 a or the pitch length B of the images 3 a.

Further, although the images 3 a are formed so as to substantially correspond to the cylindrical lenses 1 a, respectively, one-on-one in a repeated manner, since the arrangement pitch length A of the cylindrical lenses 1 a and the pitch length B of the images 3 a differ from each other, the corresponding positions therebetween will gradually shift from each other. Thus, in this meaning, the cylindrical lenses 1 a and the images 3 a do not correspond actually one-on-one. The difference between the arrangement pitch length A of the cylindrical lenses 1 a and the pitch length B of the images 3 a makes it possible to observe the smooth virtual images.

(Embodiment of Image Display Sheet)

An embodiment of an actual image display sheet will be described hereunder, in which design examples of respective portions in a case when a virtual image of eye is observed will be explained.

Dimensions of the respective structural portions of the image display sheet are as follows.

Thickness of lenticular lens 1 a: 0.45 mm

Arrangement pitch length A of cylindrical lenses: 336 μm

Pitch length B of images 3 a: 330 μm

Difference between pitch lengths A and B: 6 μm

Width C of image 3 a: 225 μm

Height D of image 3 a: 12.7 mm

Pitch length x of virtual image: 19 mm

Width y of virtual image 4: 12.7 mm

Height z of virtual image 4: 12.7 mm

(Other Embodiment 1)

An image display sheet 1 according to another one embodiment 1 has a structure capable of observing one virtual image. Further, descriptions concerning the similar structure of the embodiment mentioned above will be omitted herein.

FIG. 5 is a diagram showing a structure or configuration of an image display sheet according to the other embodiment 1, in which the corresponding relationship between respective cylindrical lenses 5 a of a lenticular sheet 5 and images 6 a, 6 b are shown. FIG. 6 is a view explaining a pitch length measurement of the image 6 b. FIG. 7 is a view explaining a virtual image according to the other embodiment 1. Further, since the structure or configuration of the lenticular sheet 5 is similar to the lenticular sheet 1 mentioned hereinabove, the explanation thereof is now omitted herein.

On the image forming layer 6, a predetermined number of images as image group for virtual image observation are formed. The image 6 a near the center of the image group is an image having no cutout, and each of other images 6 b excluding the image 6 a near the center has a cutout 6 c on a side of the image 6 a near the central portion. The images 6 a and 6 b are formed so as to correspond to the cylindrical lenses 5 a, respectively, substantially one-on-one.

In an example shown in FIG. 5, the image group is composed totally of eleven (11) images including one image 6 a near the central portion and ten (10) images 6 b having cutouts 6 c. The cutouts 6 c become wider apart from the central image 6 a towards laterally apart direction on the drawing. Further, although, in FIG. 5, only one image 6 a at the central portion is shown, a plurality of images 6 a may be adopted.

The images 6 a and 6 b are formed, as mentioned hereinbefore with reference to the embodiment, so as to substantially correspond to the cylindrical lenses 5 a, respectively, one-on-one. Further, an image display sheet is constructed so that a ratio of difference between a pitch length A of arrangement of the adjacent cylindrical lenses 5 a and a pitch length B of the images 6 a and 6 b satisfies that the difference is within a range of 0% to 10% with respect to the arrangement pitch length A of the cylindrical lenses 1 a or the pitch length B of the images 6 a and 6 b.

It is herein noted that the pitch length B between the images 6 a and 6 b and the pitch length B between the images 6 b are deemed as the pitch length B in a case of supposing that the image 6 b is not provided with a cutout (FIG. 6).

Furthermore, the widths y and z of the observed virtual image will be determined on the basis of the equations (2) and (3) described hereinbefore. The width C and D are ones in a case of supposing that the images 6 b have no cutout (FIG. 6). In a case when the widths C and D are obtained from the image 6 b with no cutout, the lateral size of the image 6 a is determined as the width C and the vertical size thereof is the height D.

Further, the image forming layer 6 may be formed to an image forming medium, not shown, and also, as in another embodiment 2 described herein after, may be formed directly to the lenticular sheet 5. In the case when the image forming layer 6 is formed on the image forming medium, the image forming medium has a structure or configuration identical to the image forming medium 2 described hereinbefore.

According to the structure mentioned above, an image display sheet 200 capable of observing only one virtual image 7 as shown in FIG. 7 can be realized. When a line of sight is being moved by changing a viewer's observing angle, one virtual image 7 in which the central image is distinctively displayed is observed as pseud moving image (graphics) based on the images 6 a and 6 b formed to the image forming layer and the cylindrical lenses 5 a.

(Embodiment of Image Display Sheet)

An embodiment of an actual image display sheet according to another embodiment 1, in which design examples of respective portions in a case when a virtual image of eye is observed, will be explained.

Dimensions of the respective structural portions of the image display sheet are as follows.

Thickness of lenticular lens 1 a: 0.45 mm

Arrangement pitch length A of cylindrical lenses: 336 μm

Pitch length B between images 6 a and 6 b (and between 6 b and 6 b): 330 μm

Difference between pitch lengths A and B: 6 μm

Width C of image 6 a (and 6 b): 225 μm

Height D of image 6 a (and 6 b): 12.7 mm

Width y of virtual image 7: 12.7 mm

Height z of virtual image 7: 12.7 mm

(Other Embodiment 2)

FIG. 8 is a sectional view of an image display sheet according to other embodiment 2. In this other embodiment 2, an image display sheet 300 has a structure in which an image forming layer is formed to a lenticular sheet.

As shown in FIG. 8, the image display sheet 300 is provided with a lenticular sheet 8 and an image forming layer 9 as essential elements. The structure of the lenticular sheet 8 is the same as that of the lenticular sheet 1 mentioned hereinbefore, so that the description thereof is omitted herein.

The image forming layer 9 is a layer on which images 9 a such as pictures, letters or like as images for virtual image observation is printed or transferred. The image forming layer 9 is provided on the surface on the side opposite to the surface on which convex-shaped cylindrical lenses 8 a of the lenticular sheet 8. Although a material of the image forming layer 3 is not specifically limited, as far as the material is adhesive to the lenticular sheet 8, for example, known material for ink, and such material for ink may include light storage ink or fluorescent ink.

On the image forming layer 9, a plurality of images 9 a are formed repeatedly so as to substantially correspond to the cylindrical lenses 8 a one-on-one. Further, an image display sheet is constructed so that a ratio of difference between a pitch length A of arrangement of the cylindrical lenses 8 a and a pitch length B of the images 9 satisfies that the difference is not more than 10% with respect to the arrangement pitch length A of the cylindrical lenses 8 a or the pitch length B of the images 9. The other structures of the embodiment 2 are similar to those of the image forming layer 3 or the image forming layer 6, so that the explanations thereof are omitted herein. As mentioned above, the image forming layer 3 or the image forming layer 6 may be formed directly to the lenticular sheet 8.

(Other Embodiment 3)

It may be possible to combine the image display sheet with a stereoscopic viewing sheet. As such embodiment in which the image display sheet is combined with a stereoscopic viewing sheet will be explained as the other embodiment 3.

FIG. 9 is a view for explaining a structure of an image display sheet according to the other embodiment 3. FIG. 10 is a plan view of an image forming layer. FIG. 9 shows a section of an image display sheet 400, which is composed of a virtual image display portion 40 a and an image display portion 40 b to be observed.

The virtual image display portion 40 a is composed of the lenticular sheet 10 common to the display portion 40 b of the image to be observed, an image forming medium 11 common to the display portion 40 b of the image to be observed, and the image forming layer 12. The display portion 40 b of the image to be observed (image display portion 40 b for observation) is composed of the lenticular sheet 10 common to the virtual image display portion 40 a, the image forming medium 11 common to the virtual image display portion 40 a, and the image forming layer 13.

The lenticular sheet 10 has a structure similar to that of the lenticular sheet 1 mentioned above, the image forming medium 11 has a structure similar to that of the image forming medium 2 mentioned above, and the image forming layer 12 has a structure similar to that of the image forming layer 3 or image forming layer 6 mentioned above, so that the explanations thereof will be omitted herein. Further, in examples shown in FIGS. 9 and 10, images 12 a as images for virtual image observation are formed on the image forming layer 12.

The image forming medium 11 is an image forming medium common to the virtual image display portion 40 a and the image display portion 40 b for observation. The image forming layers 12 and 13 are formed on the side of the lenticular sheet 10. The other structures of the image forming medium 11 are substantially identical or similar to that of the image forming medium 2 mentioned hereinbefore, and accordingly, the explanation thereof will be omitted herein.

The image display portion 40 b for observation has substantially the same structure of the conventionally known lenticular display body and attains substantially the same effect as that attained thereby. The image forming layer 13 of the image display portion 40 b for observation is a layer on which single or a plurality of other images, different from the image for observing the virtual image (image 12 a in the present embodiment) are printed or transferred. The other images may herein include images for stereoscopic view, images for changing, and images picture patterns or letters or like as images of animation. In the example of FIG. 10, images 13 a for left eye and images 13 b for right eye displaying the images to be observed acting in association with the cylindrical lenses 10 a of the lenticular sheet 10 are arranged in form of stripe. A material for the image forming layer 13 is not specifically limited as far as it closely adheres to the image forming medium 11, and for example, a conventionally known ink material or like will be used.

The lamination of the lenticular sheet 10 and the image forming medium 11 is performed by known adhesion method or sticking method in accordance with materials forming the image forming medium 11 and the image forming layers 12 and 13 with the transparency of the lenticular sheet 10 and the image forming layers 12 and 13 being maintained.

When an observer moves his (or her) line of sight by changing viewing angle from an upper position of the lenticular sheet 10, a virtual image is observed on the virtual image display portion 40 a in associated action between the image of the image forming layer 12 and the cylindrical lens 10 a, and an image for observing for virtual image is observed on the image display portion 40 b for observation in associated action between the image of the image forming layer 13 and the cylindrical lens 10 a.

As explained hereinabove, according to the present embodiment, the image display sheet 400 in combination of the virtual image display portion 40 a capable of observing the virtual image and the image display portion 40 b for observation capable of observing the image to be observed (observed image) can be constructed. Further, it is to be noted that although, in the explanations made with reference to FIGS. 9 and 10, a case of only two virtual image display portions 40 a and three image display portions 40 b for observation was exemplarily described for the sake of simple and easy understanding, a desired number of (plural or single) virtual image display portions 40 a and a desired number of (plural or single) image display portion 40 b for observation may be combined in accordance with the demand of design for the image display sheets.

According to the image display sheet 400 of the other embodiment 3, since the virtual image display portions 40 a and the image display portions 40 b for observation are composed of the same image forming medium 11, a stable image display sheet can be realized more easily. For example, in a case when an image display sheet on which a face of “kabuki” actor is displayed will be prepared, both eye portions are formed by the virtual image display portions 40 a and portions other than both eyes are formed by the image display portions 40 b for observation to thereby display the stereoscopic face of the “kabuki” actor in which only both eyes can be smoothly moved.

Further, in FIGS. 9 and 10, the image display portion 40 b for observation is composed as a conventionally known lenticular display portion and constructed so that the stereoscopic image to be observed can be observed by the associated action between the images of the image forming layer 13 and the cylindrical lenses 10 a. However, the present invention is not limited to such structure or configuration, and for example, a two-dimensional image, such as illustration, image of face, face picture or like, which is not an image attaining a specific effect by such as stereoscopic image or changing image in the associated action with a cylindrical lens, may be formed as the image display portion 40 b for observation. For example, the two-dimensional image may be an image as a back scene of the virtual image display portion 40 a. For example, in a case of using for position detection, an identification image such as bar-code, two-dimensional code or like for identifying the image display sheet to the camera may be utilized. In the case of the two-dimensional image, the lenticular sheet 10 may not be provided for the image display portion 40 b for observation.

(Other Embodiment 4)

According to the present embodiment, an image display sheet may be formed using a flat convex lens sheet. Hereafter, a case in which a flat convex lens sheet is used will be explained as the other embodiment 4.

FIG. 11 is a sectional view representing an image display sheet 500 according to the other embodiment 4. The image display sheet 500 is composed of a flat convex lens sheet 15 and an image forming layer 17 as essential components. Herein, an example in which an image forming layer 16 is formed to an image forming medium such as paper will be described. Respective layers constituting the image display sheet 500 will be explained hereunder.

The flat convex lens sheet 15 is formed by arranging a plurality of flat convex lenses 15 a in form of honeycomb shape or square shape in a plan view. The flat convex lenses 15 a are shown in an upper portion on the drawing of FIG. 11, for example. Further, although a material for the flat convex lens sheet 15 is not limited to specific one as far as a lens sheet which has been conventionally used as an image display sheet, a transparent resin material such as PET (polyethylene terephthalate), PP, PETG (glycol-denatured polyethylene terephthalate), acryl, acrylate series resin or like.

The image forming medium 16 is disposed on a side of the flat convex sheet 15 on which convex-shape is not formed, and the image forming layer 17 is formed on the flat convex sheet 15 side of the image forming medium 16. The other structures of the image forming medium 16 are substantially identical to those of the image forming medium 2 mentioned hereinbefore, so that the explanation thereof will be omitted herein.

The image forming layer 17 is a layer formed by printing or transferring an image 17 a of a picture pattern or a letter as an image for virtual image observation. The image forming layer 17 is provided for the image forming medium 16 on the side of the flat convex lens. A material for the image forming layer 17 is not limited as far as the material closely adheres to the image forming medium 16, and for example, a conventionally known ink material may be utilized. The material for ink may include light storage ink or fluorescent ink. The other structures of the image forming layer 17 are substantially identical to those of the image forming layer 3 mentioned hereinbefore, so that the explanation thereof will be omitted herein.

A pint face of the flat convex lens 15 a is on the image forming layer 17. In other words, the flat convex lens 15 a is constructed so that a focal point thereof accords with the image 17 a. Further, the lamination of the flat convex sheet 15 and the image forming medium 16 to which image forming layer 17 is provided is performed by a known adhesion method or sticking method in accordance with materials forming the image forming medium 16 and the image forming layer 17 with the transparency of the flat convex sheet 15 and the image forming layer 17 being maintained. Namely, it may be allowed for the flat convex sheet 15 to have a structure in which the image 17 a formed to the image forming layer 17 can be observed by the observer from the side having the convex shape of the flat convex lens 15 a of the flat convex sheet 15. More specifically, it may be allowed for the flat convex sheet 15 to have a structure in which a virtual image with the movement, or movement and deformation based on the image 17 a formed to the image forming layer 17 can be observed.

FIG. 12A is a view for explaining a structure of the image display sheet according to the other embodiment 4. FIG. 12A is a plan view of the flat convex lens sheet, and FIG. 12B is a plan view of the image forming layer. FIG. 13 and FIG. 14 are views for explaining the structure of a virtual image according to the other embodiment 4.

The flat convex sheet 15 is formed with a plurality of flat convex lenses 15 a. FIG. 12A shows an example of the flat convex lens sheet having honeycomb arrangement. As shown in FIG. 12B, a plurality of images 17 a are formed to the image forming layer 17. The images 17 a are formed in a repeated arrangement so as to substantially correspond to the flat convex lenses 15 a, respectively, one-on-one. In the examples of FIGS. 12A and 12B, images 17 a of thirty (30) eyes correspond respectively to the flat convex lenses 15 a one-on-one.

The flat convex display sheet is constructed so that a ratio of difference between a pitch length of arrangement of the flat convex lenses 15 a and a pitch length of the images 17 a satisfies that the ratio of difference is not more than 10% with respect to the pitch length of the flat convex lenses 15 a or the pitch length of the images 17 a. In the examples of FIGS. 12A and 12B, the transverse arrangement pitch length A₁ (in figure) of the flat convex lenses 15 a (horizontal direction) and the transverse pitch length B₁ of the images 17 a differ from each other, and the ratio of difference is not more than 10% with respect to the pitch length A₁ of the flat convex lenses 15 a or the pitch length B₁ of the images 17 a. In addition, the vertical arrangement pitch length A₂ (in figure) of the flat convex lenses 15 a (vertical direction) and the vertical pitch length B₂ of the images 17 a differ from each other, and the ratio of difference is not more than 10% with respect to the pitch length A₂ of the flat convex lenses 15 a or the pitch length B₂ of the images 17 a.

That is, in a case where the pitch length B₁(B₂) of the images 17 a is smaller than the arrangement pitch A₁(A₂) of the flat convex lenses 15 a (A₁>B₁ and A₂>B₂), the virtual image 18 based on the flat convex lenses 15 a and the images 17 a will be observed stereoscopically for the observer in a manner such that the virtual image 18 goes down below the flat convex lens sheet 15. In this case, when the line of sight of the observer is moved rightward, the virtual image 18 is observed as is also moved rightward, and on the other hand, when the line of sight of the observer is moved leftward, the virtual image 18 is observed as is also moved leftward. That is, the virtual image 18 is observed in the same direction as the moving direction of the line of sight of the observer.

On the other hand, in the case the pitch length B₁ (B₂) of the images 17 a is not less than the pitch length A₁ (A₂) of the arrangement of the flat convex lenses 15 a (A₁<B₁ and A₂<B₂), the virtual image 18 based on the flat convex lenses 15 a and the images 17 a will be observed stereoscopically for the observer in a manner such that the virtual image 18 goes up above the flat convex lens 15. In this case, when the line of sight of the observer is moved rightward, the virtual image 18 is observed as is moved leftward, and on the other hand, when the line of sight of the observer is moved leftward, the virtual image 18 is observed as is moved rightward. That is, the virtual image 18 is observed in the direction reverse to the moving direction of the line of sight of the observer.

Further, in order to observe the virtual image moving smoothly, it may be preferred to take construction in a manner such that, in a case where the arrangement pitch length A of the flat convex lens 15 a is in a range of 195 μm and 180 μm, a ratio of difference between the arrangement pitch length A of the flat convex lens 15 a and the pitch length B of the image 17 a differs in a range of 0.01% and 5%. In a more specific explanation along the difference in the line of sight movement, in order to observe the virtual image 18 moving smoothly, it may be preferred that the pitch length B of the image 17 a is in a range of 99.99% to 95.00% of the arrangement pitch length A of the flat convex lens 15 a, and more preferably, in a range of 99.50% to 97.00% thereof. Further, in order to observe the virtual image 18 moving in a direction reverse to moving direction of the line of sight, it may be preferred that the pitch length B of the image 17 a is in a range of 100.01% to 105.00% of the arrangement pitch length A of the flat convex lens 15 a, and more preferably, in a range of 100.50% to 103.00% thereof.

As shown in FIGS. 13 and 14, as an observer changes his (her) line of sight by changing the viewing angle, the virtual image 18 based on the image 17 a formed to the image forming layer 17 and the flat convex lens 15 a can be observed from an upper side. FIG. 13 shows a state of the virtual image in a case where the line of sight is moved in a horizontal direction, and FIG. 14 shows a state of the virtual image in a case where the line of sight is moved in a vertical direction.

A pitch length “x₁” of the virtual image 18 shown in FIG. 13 is determined by the equation (1). A width “y₁” of the virtual image 18 in the horizontal direction is determined by the equation (2). Herein, the character “A” is the pitch length A₁ of the arrangement of the flat convex lenses 15 a, the character “B” is the pitch length B₁ of the images 17 a in the horizontal direction, the character “C” is a width C₁ (lateral size) of the image 17 a in the horizontal direction of the images 17 a.

A pitch length “x₂” of the virtual image 18 shown in FIG. 14 is determined by the equation (1). A width “y₂” of the virtual image 18 in the vertical direction is determined by the equation (2). Herein, the character “A” is the pitch length A₂ of the arrangement of the flat convex lenses 15 a, the character “B” is the pitch length B₂ of the images 17 a in the vertical direction, the character “C” is a height C₂ (vertical size) of the image 17 a in the vertical direction of the images 17 a.

Further, in the equations (1) and (2), while the value |A−B| becomes smaller, the moving speed with respect to the movement of the line of sight of the observer becomes faster. Therefore, it is preferred that the value |A−B| is set in accordance with the use condition of the image display sheet 500, that is, in view of speed of the movement of the line of sight of the actual observer. In other words, it is preferred that the moving speed of the virtual image 18 is set so as to accord with the speed of the line of sight of the observer when the observer observes the virtual image 18 by moving his (her) line of sight.

According to the structures mentioned above, the image display sheet from which the smoothly moving virtual images can be observed by using the flat convex lens sheet. As the observer moves his (her) line of sight by changing the viewing angle, the virtual image 18 based on the images 17 a formed to the image forming layer 17 and the flat convex lenses 15 a.

Further, in the described embodiment, although the image forming layer 17 is formed to the image forming medium 16, the image forming layer 17 may be formed directly on a surface opposite to the surface to which the flat convex lens of the flat convex lens sheet 15 as being made with reference to the other embodiment 2 described hereinbefore. Moreover, the image display sheet 500 may be constructed so that the images to be observed can be observed by the function based on the combination with a conventionally known stereoscopic viewing sheet with reference to the other embodiment 3 and the stereoscopic image, changing image, or animation image, or combination thereof. In such case, the images 17 a function as images for the virtual image observation.

Furthermore, the image display sheet 500 may form an image display sheet for observing one virtual image on the basis of the other embodiment 1, which may be explained hereunder as the other embodiment 5.

(Other Embodiment 5)

An image forming layer in a case where only one virtual image is observed by using a flat convex lens sheet will be explained. It is further to be noted that a flat convex lens sheet and an image forming medium have the same or similar structures as those of the other embodiment 4.

FIG. 15 is a plan view representing an image forming layer of an image display sheet according to the other embodiment 5.

Predetermined number of images 19 a and 19 b as image group for virtual image observation are formed on an image forming layer 19. An image 19 a disposed near a central portion of the image group is an image having no cutout, and other images 19 b than the central one 19 a each has a cutout 19 c on the central image 19 a side. The images 19 a and 19 b are formed so as to substantially correspond to a flat convex lens, not shown, one-on-one.

In the embodiment shown in FIG. 15, the image group is composed of the image 19 a formed near the central portion of the image forming layer 19 and a plurality of images 19 b having cutouts 19 c. The cutout 19 c of the image 19 b becomes lager as the location of the images 19 b becomes apart from the central image 19 a. Further, in the example of FIG. 15, although one image 19 a near the central portion is referred to, a plurality of images 19 a may be formed near the central portion of the image forming layer 19.

The flat convex display sheet is constructed so that a arrangement pitch length of the flat convex lenses and pitch lengths of the images 19 a and 19 b differs and a ratio of difference between the arrangement pitch length of the flat convex lenses and the pitch lengths of the images 19 a and 19 b satisfies that the ratio of difference is not more than 10% with respect to the pitch length of the flat convex lenses or the pitch length of the images 19 a and 19 b. Specifically, it is constructed that the transverse arrangement pitch length A₁ of the flat convex lenses (horizontal direction) and the transverse pitch length B₁ of the images 19 a differ from each other so that the ratio of difference therebetween is not more than 10% with respect to the pitch length A₁ of the flat convex lenses or the pitch length B₁ of the images 19 a. In addition, the vertical arrangement pitch length A₂ of the flat convex lenses in the vertical direction and the vertical pitch length B₂ of the images 19 a differ from each other so that the ratio of difference is not more than 10% with respect to the pitch length A₂ of the flat convex lenses or the pitch length B₂ of the images 19 a. Further, the pitch length B₁ and B₂ between the image 19 a and the image 19 b, and the pitch length B₁ and B₂ between the images 19 b are supposed to the pitch length B₁ and B₂ between the images 19 b in a case of no formation of cutout 19 c to the image 19 b.

A pitch length “x₁” of the virtual image, not shown, in the horizontal direction is determined by the equation (1). A width “y₁” of the virtual image in the horizontal direction is determined by the equation (2). Herein, the character “A” is the pitch length A₁ of the arrangement of the flat convex lenses, the character “B” is the pitch length B₁ of the images 19 a and 19 b in the horizontal direction, the character “C” is a width C₁ (lateral size) of the image 19 a and 19 b in the horizontal direction.

A pitch length “x₂” of the virtual image, not shown, in the vertical direction is determined by the equation (1). A width “y₂” of the virtual image in the vertical direction is determined by the equation (2). Herein, the character “A” is the pitch length A₂ of the arrangement of the flat convex lenses, the character “B” is the pitch length B₂ of the images 19 a and 19 b in the vertical direction, the character “C” is a height C₂ (vertical size) of the image 19 a and 19 b in the vertical direction.

According to the structure explained hereinbefore, the image display sheet capable of observing only one virtual image smoothly moving by using the flat convex lenses can be realized. As a viewing line (line of sight) of the observer moves by changing the viewing angle of the observer, one virtual image, in which the central image is extremely remarkably displayed, can be observed based on the images 19 a, 19 b formed on the image forming layer 19 and the flat convex lenses.

It is further to be noted that the above-mentioned embodiments may be executed by respectively combining them. For example, as to the other embodiment 3, the image forming layer may be directly formed on the surface opposite to the surface on which convex shape of the cylindrical lens of the lenticular sheet is formed in accordance with the other second embodiment. Furthermore, as to the other embodiments 4 and 5, the image forming layer may be directly formed on the surface opposite to the surface having the convex shape of the flat convex lenses of the flat convex lens sheet in accordance with the other second embodiment.

In the embodiments described above, although the examples are explained with the eye is an image for observing a virtual image (an image for observing virtual image), virtual images based on images of various picture patterns, letters and the like without limiting to the eyes can be observed. Especially, as an image for observing a virtual image, by using images of opened eye and closed eye, a virtual image with variation of opening/closing eyes can be observed. Moreover, various kinds or modes of virtual images with motion and variation can be realized by forming mouth opening/closing images or flower opening/closing images, or the like as images for observing virtual image. Hereunder, a case in which an image of an arrow is made as an image for observing virtual image will be explained with reference to FIG. 16.

(Other Embodiment 6)

FIGS. 16A and 16B are plan views representing an image forming layer of an image display sheet according to the other embodiment 6. FIGS. 16A and 16 b are examples of the image forming layer in which arrows are made as virtual image observation image.

On an image forming layer 20 shown in FIG. 16A, a plurality of images 20 a are formed as images for observing virtual images. The images 20 a are formed in a repeated manner so as to be coincident with the cylindrical lenses, not shown, of the lenticular sheet approximately one-on-one arrangement. The arrangement pitch length of the cylindrical lenses and the pitch length B of the images 20 a are made to be different so that the ratio of difference therebetween is not more than 10% with respect to the arrangement pitch length of the cylindrical lenses or pitch length B of the images 20 a. Further, the image forming layer 20 may be formed to an image forming medium, not shown, or formed directly on the lenticular sheet as in the other embodiment 2. In the case where the image forming layer 20 is formed on the image forming medium, the image forming medium may have a structure substantially the same as or identical to the image forming medium 2 mentioned hereinbefore.

A virtual image showing an arrow based on the image 20 a and the cylindrical lenses are observed from the upper side as a pseudo moving image. In addition, by appropriately adjusting or changing the arrangement pitch length, the pitch length B of the image 20 a, the width C in the arrangement direction of the cylindrical lenses of the image 20 a, and the height D of the image 20 a, the size of the virtual image to be observed based on the equations (1) to (3) mentioned hereinbefore can be freely set.

A plurality of images 21 a as images for observing virtual image are formed on an image forming layer 21 shown in FIG. 16B. The configuration of the image 21 a is substantially the same as or identical to that of the image 20 a, and hence, the explanation thereof is omitted herein.

A virtual image showing an arrow based on the image 21 a and the cylindrical lens, not shown, can be observed from an upper side of the lenticular sheet as a pseudo moving image. In addition, by appropriately adjusting or changing the arrangement pitch length, the pitch length B of the image 21 a, the width C in the arrangement direction of the cylindrical lenses of the image 21 a, and the height D of the image 21 a, the size of the virtual image to be observed based on the equations (1) to (3) mentioned hereinbefore can be freely set.

In a case where the pitch length B of the images 20 a (or 21 a), is smaller than the arrangement pitch A, not shown, of the flat cylindrical lenses (A>B), a virtual image representing an arrow based on the cylindrical lenses and the images 20 a (or 21 a) will be observed stereoscopically in a going down fashion of the lenticular sheet by an observer. In this case, when the line of sight of the observer is moved rightward, the virtual image representing an arrow is observed as is also moved rightward, and on the other hand, when the line of sight of the observer is moved leftward, the virtual image representing an arrow is observed as is also moved leftward. That is, the virtual image representing an arrow is observed in the same direction as the moving direction of the line of sight of the observer, and accordingly, it can be effectively utilized for the induction in the advancing direction.

On the other hand, in the case the pitch length B of the images 20 a (or 21 a) is larger than the arrangement pitch length A, not shown, of the cylindrical lenses (A<B), the virtual image representing an arrow based on the cylindrical lenses and the images 20 a (or 21 a) will be observed stereoscopically in a going up fashion by the observer. In this case, the virtual image rotated by 180 degrees of the images 20 a (or 21 a) will be observed by the observer. And when the line of sight of the observer is moved rightward, the virtual image representing an arrow is observed as is moved leftward, and on the other hand, when the line of sight of the observer is moved leftward, the virtual image representing an arrow is observed as is moved rightward. That is, the virtual image representing an arrow is observed in the direction reverse to the moving direction of the line of sight of the observer and accordingly, it can be effectively utilized for the induction in the direction reverse to the advancing direction.

Other lenses may be provided above the lenticular sheet, which will be explained hereunder with reference to the drawings accompanied.

(Other Embodiment 7)

An image display sheet of the other embodiment 7 has a structure in which other lenses are provided above a lenticular sheet. The other lenses, for example, are flat convex lenses, meniscus lenses, Fresnel lenses or like. It is further to be noted that descriptions of the same or identical structure as or to that of the above-mentioned embodiments will be omitted herein.

FIG. 17 is a view for explaining a structure of an image display sheet according to the other embodiment 7, and FIG. 17 is a sectional view thereof. The image display sheet 600 is provided, as essential components, with a lenticular sheet 61, an image forming layer 63 and a flat convex lens 64 as another convex lens.

The lenticular sheet 61 is composed of a plurality of cylindrical lenses 61 a arranged side by side. The image forming medium 62 is disposed to a side of the lenticular sheet 61 on which convex-shape of cylindrical lenses is not formed, and the image forming layer 63 is formed on the lenticular sheet 61 side. The image forming layer 63 is a layer in which images 63 a of picture pattern or letter as images for observing a virtual image are printed or transferred. The image forming layer 63 is provided for the image forming medium 62 on the lenticular sheet 61 side.

A flat convex lens 64 is disposed to the lenticular sheet 61 on the side of the cylindrical lenses 61 a having convex shape. The flat convex lens 64 has a convex (protruded) shape on the side opposite to the lenticular sheet 61 (i.e., upper side in FIG. 17). Further, although a material for the flat convex lens 64 is not limited to specific one, a transparent resin material such as glass, PET (polyethylene terephthalate), PP, PETG (glycol-denatured polyethylene terephthalate), acryl, acrylate series resin or like.

FIG. 18 is a sectional view showing an essential portion of the lenticular sheet for showing a focusing condition thereof. A focal point by a single cylindrical lens 61 a is converged at a point below the image forming layer 63. According to the functions of such cylindrical lenses 61 a and the flat convex lens 64, the image display sheet of the present embodiment is constructed so that the focal point from the upper portion of the flat convex lens 64 accords with an image 63 a formed on the image forming layer 63.

It is further to be noted that the other structure or configuration of the lenticular sheet 61 is substantially the same as that of the lenticular sheet 1 mentioned hereinbefore, and in addition, the structure of the image forming medium 62 is substantially the same as that of the image forming medium 2 mentioned hereinbefore, and the structure of the image forming layer 63 is substantially the same as that of the image forming layer 3 or image forming layer 6 mentioned hereinbefore.

As explained hereinabove, in the present embodiment, the flat convex lens 64 is provided as the other lens on the side of the cylindrical lenses 61 a, at which the convex portions are formed, of the lenticular sheet 61 so that the focus accords with the image 63 a through the flat convex lens 64 and the cylindrical lenses 61 a. According to such arrangement, or structure, in a case when the position detection is performed based on the virtual image by using the other lenses, it becomes possible to finely adjust the position of the virtual image by finely adjust the central position of the flat convex lens 64 to be displaced in parallel with the image display sheet 600. It is prevented for an observer to directly touch the surface of the cylindrical lenses 61 a of the lenticular sheet 61, thus attaining the function as protecting member. In addition, in a case of a virtual image being an eye, in accordance with the shape of the flat convex lens 64, an image display sheet 600 visually and sensitively approximated to the eye may be composed.

Further, in the example of FIG. 17, the flat convex lens 64 of the image display sheet 600 is constructed in a manner of being apart from the cylindrical lenses 61 a of the lenticular sheet 61 by a predetermined distance, but in the present invention, the flat convex lens may be arranged in contact to the cylindrical lenses 61 a on the upper surface thereof.

Although, with the other embodiment 7, there is explained an example using the flat convex lens, the present invention is not limited to the flat convex lens. As long as it is possible to make the focus accord with an image of the image forming layer by acting together with the cylindrical lens, for example, a convex-shaped glass plate, a plastic plate, meniscus lens, Fresnel lens or like may be used. Moreover, it may be possible to form the image forming layer directly on the lenticular sheet in accordance with the other embodiment 2 mentioned hereinabove. In addition, it may be possible to constitute an image to be observed to be capable of being observed in combination with a conventionally known stereoscopic sheet in accordance with the other embodiment 3 mentioned hereinabove, a stereoscopic image, changing image or animation image, or combination thereof.

Furthermore, it may be possible to use the flat convex lens in accordance with the other embodiments 4 and 5 mentioned hereinabove. Still furthermore, although, in the other embodiment 7 mentioned above, it is constructed that the convex surface of the flat convex lens is opposed to the lenticular sheet (upper side in the drawing), it may be possible to constitute such that the convex surface of the flat convex lens is faced to the lenticular sheet side (lower side in the drawing) as long as the focus makes coincident with the image of the image forming layer in associated function with the cylindrical lens. In the case when the flat convex lens is used in accordance with the other embodiments 4 and 5 mentioned hereinbefore, it may be also possible to position the convex surface of the flat convex lens to be opposed to the flat convex lens sheet or to face the flat convex sheet side.

(Other Embodiment 8)

An image display sheet according to the other embodiment is constituted so that a virtual image smoothly moving in accordance with the line of sight of an observer is to be made stationary. Further, the structures same as or similar to those of the above-mentioned embodiments will be omitted in description herein.

FIG. 19A is a view explaining a structure of an image display sheet according to the other embodiment 8, which represents correspondence between a lenticular sheet 111 and respective cylindrical lenses 111 a and images 113 a, 113 b. Further, it is to be noted that the structure or arrangement of the lenticular sheet 111 is substantially the same as that of the lenticular sheet 1, so that explanation thereof will be omitted herein.

On the image forming layer 113, a plural number of images 113 a and 113 b as image groups for observation of virtual images (called group of image for observing virtual image, hereunder) are formed. The group of image for observing virtual image includes groups of the image for observing stand still (stationary) virtual image which constituted by a predetermined number (for example, several tens) of images for observing stand still virtual image.

The image 113 b as the image for observing stand still virtual image is one constituting a virtual image to become stationary. In an example of FIG. 19A, groups of image for observing stand still virtual image composed of eight images 113 b are formed on both end portions of group of image for observing virtual image for the sake of simplified illustration. The images 113 a and 113 b are formed in a repeated manner so as to correspond to the cylindrical lenses 1 a substantially one-on-one.

The image 113 b will be explained hereunder. FIG. 19B is an explanation view of original images 113Xa and 113Xb. FIGS. 19C and 19D represent examples of preparation of group of image for observing stand still virtual image. Further, the image 113 a, which is not image for observing stand still virtual image, in the images for observing virtual image formed on the image forming layer 113 has the same or identical structure of the image 3 a mentioned hereinbefore, and hence, the explanation thereof is omitted herein.

In the example of FIG. 19B, the image 113 b is composed of two elements of black circle and white circle. The original image 113X of the image 113 b is composed of an original image 113Xa as an origin of the black circle and an original image 113Xb as an origin of the white circle. The image 113 b includes a cut-out portion 113 c and an enlarged portion 113 b respectively to the original images 113Xa and 113Xb, and then reduced in predetermined sizes.

Definition of a plurality of auxiliary lines to the original image 113X will be explained. For example, definitions of auxiliary lines 113 e for number of images 113 b constituting the group of image for observing stand still virtual image and auxiliary lines 113 e for preparing an enlarged portion 113 d to the image 113 b will be made. In the case of FIG. 19A, the group of image for observing stand still virtual image at the left end side of the image forming layer 113 is composed of six images 113 b, and accordingly, six auxiliary lines 113 e and two auxiliary lines 113 e forming the enlarged portion 113 d, i.e., total eight auxiliary lines (113 e(1), 113 e(2), 113 e(8)) will be defined. The respective auxiliary lines are arranged with equal interval or irregular interval.

Further, the enlarged portion 113 d forming the image 113 b is formed on the side of the image 113 a. Because of this reason, the image 113 b constituting the group of image for observing stand still virtual image on the left side of the image forming layer 113 forms the enlarged portion 113 d using the auxiliary line 113 e(1), and the image 113 b constituting the group of image for observing stand still virtual image on the right side of the image forming layer 113 forms the enlarged portion 113 d using the auxiliary line 113 e(8).

Therefore, since the image 113 b constituting the group of image for observing stand still virtual image on the left side of the image forming layer 113 does not use the auxiliary line 113 e(8), in the initial stage, only the seven auxiliary lines 113 e(1) to 113 e(7) may be defined. Likely, the image 113 b constituting the group of image for observing stand still virtual image on the right side of the image forming layer 113 does not use the auxiliary line 113 e(1), only the seven auxiliary lines 113 e(2) to 113 e(8) may be defined. For the sake of simple explanation, a case in which eight auxiliary lines are drawn to the original image 113X will be explained regardless of the images 113 b constituting the left or right group of image for observing stand still virtual image.

Further, herein, an example, in which two auxiliary lines 113 e(1) and 113 e(8) forming the enlarged portion 113 d are made as tangential lines to the original image 113X, will be explained. Further, in the followings, the term auxiliary line 113 e may be used for explaining any one of auxiliary lines 113 e(1) to 113 e(8) or all of them totally.

FIGS. 19C and 19D represent preparation examples of groups of image for observing stand still virtual image, in which FIG. 19C represents a preparation example of the group of image for observing stand still virtual image on the left side of the image forming layer 113 shown in FIG. 19A, and FIG. 19D represents a preparation example of the group of image for observing stand still virtual image on the right side of the image forming layer 113 shown in FIG. 19A. The groups of image for observing stand still virtual image shown in FIGS. 19C and 19D will be explained with reference to examples of cases formed respectively with six images 113 b. Further, the auxiliary line 113 e and a later-mentioned intersection point P are for defining the cut-out portion 113 c and the enlarged portion 113 d, so that they are not described on the image forming layer 113.

First, refereeing to FIG. 19C, the preparation example of the group of image for observing stand still virtual image on the left side of the image forming layer 113 will be explained. At first, original images 113X of the number corresponding to the number of the images 113 b constituting the group of image for observing stand still virtual image is prepared. In the example of FIG. 19C, six original images 113X are prepared (C-1). Further, in the examples of (C-1) and (C-2) of FIG. 19C, the original images 113X are illustrated with non-color (white) manner for the sake of clear observation.

The respective original images 113X are deformed based on vertical line described to the auxiliary line 113 e(1) from the intersection points between the auxiliary lines 113 e(2) to 113 e(7) and the original images 113X. In the example of FIG. 19C, as to the respective original images 113X, the respective original images 113X are deformed based on vertical line described to the auxiliary line 113 e(1) from the intersection points P between the auxiliary lines 113 e(2) to 113 e(7) and the original images 113X (C-2). In the example of FIG. 19C, the original images 113X are composed of the original images 113Xa and 113Xb.

Accordingly, in the example of the original images 113Xa, the respective original images 113Xa are deformed based on vertical line described to the auxiliary line 113 e(1) from the intersection point P between the auxiliary lines 113 e(2) to 113 e(7) and the original images 113Xa. In the like manner, the respective original images 113Xb are deformed based on vertical line described to the auxiliary line 113 e(1) from the intersection point P between the auxiliary lines 113 e(2) to 113 e(7) and the original images 113Xb.

More specifically, as to the original image 113X, nearest to the image 113 a in the six original images 113X (most right-side original image 113X in FIG. 19C), a vertical line is drawn to the auxiliary line 113 e(1) from the two intersection points P of the auxiliary lines 113 e(2) and the original images 113Xa.

As to the original image 113X, secondarily nearest to the image 113 a in the six original images 113X, a vertical line is drawn to the auxiliary line 113 e(1) from the two intersection points P of the auxiliary lines 113 e(3) and the original images 113Xa.

As to the original image 113X, thirdly nearest to the image 113 a in the six original images 113X, a vertical line is drawn to the auxiliary line 113 e(1) from the two intersection points P of the auxiliary lines 113 e(4) and the original images 113Xa.

As to the original image 113X, fourthly nearest to the image 113 a in the six original images 113X, a vertical line is drawn to the auxiliary line 113 e(1) from the two intersection points P of the auxiliary lines 113 e(5) and the original images 113Xa.

As to the original image 113X, fifthly nearest to the image 113 a in the six original images 113X, a vertical line is drawn to the auxiliary line 113 e(1) from the two intersection points P of the auxiliary lines 113 e(6) and the original images 113Xa.

As to the original image 113X, sixthly nearest to the image 113 a in the six original images 113X, i.e., the original image on the most left side image 113X in the drawing, a vertical line is drawn to the auxiliary line 113 e(1) from the two intersection points P of the auxiliary lines 113 e(7) and the original images 113Xa.

As mentioned hereinabove, the original image 113X is deformed based on the auxiliary line 113 e(1) and the vertical line. In the example of FIG. 19C (C-3), the original image 113X is deformed based on the auxiliary line 113 e(1) and the vertical line. The original image 113X has the enlarged portion 113 d on the image 113 a side (right side in FIG. 19C). More specifically, the enlarged portion 113 d is formed by the auxiliary line 113 e(1) and the vertical line.

At least one or more images 113 b positioned on the left end side of the group of image for observing virtual image have cutouts 113 c formed at both end portions in the vertical direction with respect to the arranging direction of the images 113 a and 113 b as virtual image observation images. In the example of FIG. 19C (C-3), in the case of the original images 113Xa, when the auxiliary lines 113 e(2) to 113 e(7) having the intersection points P are positioned on the left side of the central portion (in other words, when they are positioned on the side apart from the image 113 a than the central position of the original image 113Xa), the cutouts 113 c are formed above and below the original image 113Xa. In the like manner, in the case of the original images 113Xb, when the auxiliary lines 113 e(2) to 113 e(7) having the intersection points P is positioned on the left side of the central portion (in other words, when they are positioned on the side apart from the image 113 b than the central position of the original image 113Xb), the cutouts 113 c are formed above and below the original image 113Xb.

Further, the original images 113X after the deformation are downscaled in predetermined size to thereby form the images 113 b (C-4). In the example of FIG. 19C (C-4), six images 113 b are formed.

Then, refereeing to FIG. 19D, the preparation example of the group of image for observing stand still virtual image on the right side of the image forming layer 113 will be explained. At first, original images 113X of the number corresponding to the number of the images 113 b constituting the group of image for observing stand still virtual image are prepared. In the example of FIG. 19D, six original images 113X are prepared (D-1). Further, in the examples of (D-1) and (D-2) of FIG. 19D, the original images 113X are illustrated with non-color (white) manner for the sake of clear observation.

The respective original images 113X are deformed based on vertical line described to the auxiliary line 113 e(8) from the intersection points between the auxiliary lines 113 e(7) to 113 e(2) and the original images 113X. In the example of FIG. 19D, as to the respective original images 113X, the respective original images 113X are deformed based on vertical line described to the auxiliary line 113 e(8) from the intersection points P between the auxiliary lines 113 e(7) to 113 e(2) and the original images 113X (D-2). In the example of FIG. 19D, the original images 113X are composed of the original images 113Xa and 113Xb. Accordingly, the respective original images 113Xa are deformed based on vertical line described to the auxiliary line 113 e(8) from the intersection points P between the auxiliary lines 113 e(7) to 113 e(2) and the original images 113Xa. In the like manner, the respective original images 113Xb are deformed based on vertical line described to the auxiliary line 113 e(8) from the intersection points P between the auxiliary lines 113 e(7) to 113 e(2) and the original images 113Xb.

More specifically, as to the original image 113X, nearest to the image 113 a in the six original images 113X (most left-side original image 113X in FIG. 19D), a vertical line is drawn to the auxiliary line 113 e(8) from the two intersection points P of the auxiliary lines 113 e(7) and the original images 113Xa.

As to the original image 113X, secondarily nearest to the image 113 a in the six original images 113X, a vertical line is drawn to the auxiliary line 113 e(8) from the two intersection points P of the auxiliary lines 113 e(6) and the original images 113Xa.

As to the original image 113X, thirdly nearest to the image 113 a in the six original images 113X, a vertical line is drawn to the auxiliary line 113 e(8) from the two intersection points P of the auxiliary lines 113 e(5) and the original images 113Xa.

As to the original image 113X, fourthly nearest to the image 113 a in the six original images 113X, a vertical line is drawn to the auxiliary line 113 e(8) from the two intersection points P of the auxiliary lines 113 e(4) and the original images 113Xa.

As to the original image 113X, fifthly nearest to the image 113 a in the six original images 113X, a vertical line is drawn to the auxiliary line 113 e(8) from the two intersection points P of the auxiliary lines 113 e(3) and the original images 113Xa.

As to the original image 113X, sixthly nearest to the image 113 a in the six original images 113X, i.e., the most right side original image 113X in the drawing, a vertical line is drawn to the auxiliary line 113 e(8) from the two intersection points P of the auxiliary lines 113 e(2) and the original images 113Xa.

As mentioned hereinabove, the original image 113X is deformed based on the auxiliary line 113 e(8) and the vertical line. In the example of FIG. 19D (D-3), the original image 113X is deformed based on the auxiliary line 113 e(8) and the vertical line. The original image 113X has the enlarged portion 113 d on the image 113 a side (left side in FIG. 19D). More specifically, the enlarged portion 113 d is formed by the auxiliary line 113 e(8) and the vertical line.

At least one or more images 113 b positioned on the right end side of the group of image for observing virtual image have cutouts 113 c formed at both end portions in the vertical direction with respect to the arranging direction of the images 113 a and 113 b as virtual image observation images. In the example of FIG. 19D (D-3), in the case of the original images 113Xa, when the auxiliary lines 113 e(7) to 113 e(2) having the intersection points P is positioned on the right side of the central portion (in other words, when they are positioned on the side apart from the image 113 a than the central position of the original image 113Xa), the cutouts 113 c are formed above and below the original image 113Xa. In the like manner, in the case of the original images 113Xb, when the auxiliary lines 113 e(7) to 113 e(2) having the intersection points P are positioned on the right side of the central portion (in other words, when they are positioned on the side apart from the image 113 a than the central position of the original image 113Xa), the cutouts 113 c are formed above and below the original image 113Xb.

Further, the original images 113X after the deformation are downscaled in predetermined size to thereby form the images 113 b (D-4). In the example of FIG. 19D (D-4), six images 113 b are formed.

The group of image for observing stand still virtual image are formed on the image forming layer 113 by the images 113 b formed by the manner mentioned above (FIG. 19A).

The images 113 a and 113 b are formed so as to correspond, one-on-one, to the cylindrical lenses 111 a as like as in the embodiments described hereinbefore. It is constructed such that the arrangement pitch length A of the cylindrical lenses 111 a differs from the ratio of difference between the pitch lengths B of the images 113 a and 113 b, and in addition, the difference between the arrangement pitch length A of the cylindrical lenses 111 a and the pitch length B of the images 113 a is difference is not more than 10%. Further, the pitch length B between the image 113 a and the image 113 b, and the pitch length B between the images 113 b are supposed to the pitch length B in a case of no formation of cutout 113 c and enlarged portion 113 d to the image 113 b. Moreover, the widths C and D are supposed to the widths C and D in a case of no cutout 113 c to the image 113 b.

Further, the image forming layer 113 may be formed to an image forming medium, not shown, and also, as in another embodiment 2, may be formed directly to the lenticular sheet 111. In the case when the image forming layer 113 is formed on the image forming medium, the image forming medium has a structure or configuration identical to the image forming medium 2 described hereinbefore.

As described hereinabove, since the image display sheet is formed so as to have the group of image for observing stand still virtual image composed of a predetermined number of the images 113 b formed on the end portion of the group of image for observing virtual image and also have the enlarged portion to the image 113 b, it becomes possible to stop (take stationary position) the virtual image 114 smoothly moving along the movement of the line of sight of an observer to the predetermined position. FIG. 20 is a view for explaining a configuration of a virtual image, in which (A-1)˜(A-4) shows movement of the virtual image when the line of sight is moved rightward on the image display sheet 1100. When the line of sight is moved rightward, the virtual image moves further rightward ((A-1)→(A-2)), and even if the line of sight is further moved rightward, the virtual image stops without further moving ((A-3) and (A-4)). (B-1)˜(B-4) shows movement of the virtual image when the line of sight is moved leftward on the image display sheet 1100. When the line of sight is moved leftward, the virtual image moves further rightward ((B-1)→(B-2)), and even if the line of sight is further moved leftward, the virtual image stops without further moving ((B-3) and (B-4)). As described above, by constituting the group of image for observing stand still virtual image composed of the images 113 b, an image display sheet capable of observing a stand still (stationary) virtual image can be realized.

Further, in the above-described embodiment, although there is explained an example in which the auxiliary line 113 e(1) (FIG. 19C) and the auxiliary line 113 e(8) (FIG. 19D) forming the enlarged portion 113 d are tangential lines to the original image 113X, the present invention is not limited to such example. FIG. 21 is a view for explaining an application of the other embodiment 9. In an example shown in FIG. 21, the auxiliary line 113 e(1) is defined at a position apart from the original image 113X, and the original image 113X is deformed based on the vertical line drawn to the auxiliary line 113 e(1) from the intersection point between the auxiliary lines 113 e(2) to 113 e(7) and the original image 113X. As explained above, by defining the auxiliary line 113 e(1) at the position apart from the original image 113X, further larger enlarged portion 113 d may be formed.

In the example shown in FIG. 19C, when the line of sight of an observer is moved leftward on the image display sheet 1100, the still virtual image stops (i.e., is stationary). If the line of sight is further moved leftward after the stopping of the virtual image, the stopped virtual image becomes invisible. However, with reference to an example of FIG. 21, since the image 113 b has the larger enlarged portion 113 d, even if the line of sight is continuously moved after the stopping of the virtual image, a virtual image can be observed for a time longer than the case of the image 113 b shown in FIG. 19C.

Furthermore, in the embodiment described above, although there is explained an example in which the image 113 b having the cutout 113 c and the enlarged portion 113 b are formed by using the auxiliary lines 113 e, the present invention is not limited to such example. In order for realizing the still (stationary) virtual image, the image 113 b as an image for observing stand still virtual image may be constituted so as to have at least the cutout 113 c and the enlarged portion 113 d.

Furthermore, in the embodiment described above, although there is adopted the structure having the groups of image for observing stand still virtual image composed of a predetermined number of images 113 b formed at both end portions of the group of image for observing virtual image, there may adopt a structure in which the group of image for observing stand still virtual image composed of the images 113 a is formed only one end portion thereof. For example, if a structure having the group of image for observing stand still virtual image formed on the left side of the image 113 a in FIG. 19A is for example taken, there may also be adopted a structure in which when the line of sight is moved rightward on the image display sheet 1100, the virtual image 114 is continuously moved without being stopped, and when the line of sight is moved leftward, the virtual image is moved leftward, and thereafter, stops.

Still furthermore, in the embodiment described above, although there is adopted the structure having the images 113 a as the images for observing virtual image which are not the images for observing stand still virtual image to the image forming layer 113Xa, the present invention may be realized even in the case of no images 113 a.

Still furthermore, in the embodiment described above, although the explanation is made to the manner or means in which the original images 113Xa and 113Xb are reduced in the predetermined sizes after the formation of the cutouts 113 c and the enlarged portions 113 d, the present invention is not limited to such example, and after the original images 113Xa and 113Xb are reduced in the predetermined sizes, the cutouts 113 c and the enlarged portions 113 d may be formed.

Still furthermore, in the embodiment described above, although the original images 113X are used as a manner or means for forming the cutouts 113 c and the enlarged portions 113 d, the present invention is not limited to such example, and other formation means may be adopted as far as the cutout 113 c and the enlarged portion 113 d can be formed to the image 113 b.

(Embodiment of Position Detection System)

Hereunder, a case in which the image display sheets explained in the above-mentioned respective embodiments are utilized for position detection is explained. In the present embodiment, there is explained a case, as an example of a position detection system, in which an image display sheet is attached to an object to be observed, this image display sheet is photographed, and a positional relationship between the object to be observed and a camera is detected.

FIG. 22A is a schematic view showing a position detection system S1 to which the image display sheet according to the present invention is applicable. The position detection system S1 operates to photograph an image display sheet 1000 attached to an object to be observed 3000 by a camera 2000 provided to a robot or like, not shown, after attaching the image display sheet 1000 to the object 3000. The photographed image is taken into a position detecting device 2002 constituted by a computer or like from the camera 2000 through a cable 2001. With the image taken into the position detecting device 2002, a photographed image of a portion of the image display sheet 1000 is extracted from an image obtaining portion 2003, and an operating portion 2004 operates relative positional relationship between the object to be observed 3000 and the camera 2000 based on a virtual image imaged in the photographed image, and then, detects the position of the object 3000.

The image display sheet 1000 may take any structure as long as the structure is a structure of one of the image display sheets explained in the above-mentioned embodiments or combination thereof, but herein, an image display sheet constituted to be capable of observing a virtual image by using a flat convex lens sheet as one example.

FIG. 22B is a sectional view of the image display sheet 1000, and is a view explaining correspondence between a flat convex lens 101 a and images 103A and 103B. In the image forming layer 103, a plurality of images 103A and 103B as virtual image observation images are formed by means of printing or transcription. The images 103A and 103B are arranged repeatedly so as to accord one-on-one with the flat convex lenses 101 a, respectively. It is further to be noted that the image display sheet 1000 explained in this embodiment has the same pitch of the image 103A in the perpendicular (vertical) and transverse (horizontal) (x-direction and y-direction) of the flat convex lens 101 a, and also has the same pitch of the image 103B in the perpendicular (vertical) and transverse (horizontal) of the flat convex lens 101 a. The other structures of the image display sheet 1000 are identical to those of the image display sheet 500, and accordingly, the explanation thereof will be omitted herein.

A virtual image 104A based on the flat convex lens 101 a and the image 103A and a virtual image 104B based on the image 103B are observed and photographed. The respective pitch lengths of the flat convex lenses 103 a have relationship represented by the equations (4) to (7). When the position of the camera 2000 changes (i.e., is moved) in the x-direction with respect to the object 3000 to be observed, images corresponding to virtual images 104A and 104B are moved in the x-direction and photographed. And when the position of the camera 2000 changes (i.e., is moved) in the y-direction with respect to the object 3000 to be observed, images corresponding to virtual images 104A and 104B are moved in the y-direction and photographed. Accordingly, the virtual image 104A based on the image 103A is moved faster in the virtual image movement according to the position movement of the camera than that of the virtual image 104B based on the image 103B (equation 8). According to such structure, the virtual images 104A (+mark) 104B (◯mark) respectively having different performance (displacement) with respect to the displacement of the angle θ, at which the object to be observed can be visually observed, can be observed on the image display sheet 1000. Then, it is preferred to set the respective pitches of the flat convex lenses 103 a and the images 103A, 103B in accordance with the desired positional detection performance. [Formula 2] Pitch length of image 103A<arrangement pitch length of flat convex lens 101a  equation (4) Pitch length of image 103B<arrangement pitch length of flat convex lens 101a  equation (5) Pitch length of image 103B<pitch length of image 103A  equation (6) |Pitch length of flat convex lens 101a−pitch length of image 103A|<|Pitch length of flat convex lens 101a−pitch length of image 103B|  equation (7) Moving speed of virtual image 104B<moving speed of virtual image 104A  equation (8)

FIG. 23A is a view explaining the camera position and the photographed image, and photographed images 2005 (x (−1)), 2005 (x (0)) and 2005 (x (1)) are images extracted at the image obtaining portion 2003 photographed by the camera 2000. In the photographed image 2005 (x (0)), photographed by the camera 2000 at the position (camera position 2000 (x (0)), perpendicular to the image display sheet 1000 (angle θ=0), the virtual images 104A and 104B are overlapped at the center of the images. When the camera 2000 is moved in the x-direction (camera position 2000 (x (1)) and the camera position 2000 (x (−1)), the virtual images 104A and 104B in the photographed image 2005 (x (−1)) are also moved in the same direction as the moving direction of the camera.

The operating portion 2004 operates the relative positional relationship in the x-direction between the object 3000 to be observed and the camera 2000 based on the difference Δx between the position of the virtual image 104A and the position of the virtual image 104B, and then, detects the position of the camera 2000.

The same will be applied to the case of the y-direction. FIG. 23B is a view for explaining the camera position and the photographed image and is the explanatory view relating to the y-directional movement of the camera position. In the photographed image 2005 (y (0)), photographed by the camera 2000 at the position (camera position 2000 (y (0)), perpendicular to the image display sheet 1000 (angle θ=0), the virtual images 104A and 104B are overlapped at the center of the images. When the camera 2000 is moved in the y-direction (camera position 2000 (y (1)) and the camera position 2000 (y (−1)), the virtual images 104A and 104B in the photographed image 2005 (−1)) are also moved in the same direction as the moving direction of the camera. The operating portion 2004 operates the relative positional relationship in the y-direction between the object 3000 to be observed and the camera 2000 based on the difference Δy between the position of the virtual image 104A and the position of the virtual image 104B, and then, detects the position of the camera 2000.

Further, in the above explanation, although there is explained the case in which the pitch of the image 103A is the same in the perpendicular direction and horizontal direction (x-direction and y-direction) of the flat convex lens 101 a, and the pitch of the image 103B is the same in the perpendicular direction and horizontal direction of the flat convex lens 101 a, the images may be constituted so as to provide the different pitches. Moreover, herein, although the camera position is detected by the difference Δx between the two virtual images, in the case of one virtual image, the camera position may be detected based on the difference in the moving distance from the reference position of the photographed image 2005 (x (0) (or photographed image 2005 (y (0)) at the camera position 2000 (x (0) or (camera position 2000 (y 0). The reference position is, for example, is the center of the photographed image, four corners, reference guide (explained hereinafter) or like. The same will be applied in the descriptions hereunder.

As can be understood from the above-mentioned descriptions, it will be found that the image display sheet 1000 provided for the object 3000 to be observed for the position detection can be utilized for the position detection system S1. That is, with the image display sheet 1000, a plurality of images 103A and 103B for displaying the virtual images 104A and 104B in reaction to the flat convex lenses 101 a are formed to the image forming layer 103 one-on-one in the repeated manner, the arrangement pitch length of the flat convex lens 101 a in the horizontal direction and the pitch length of the image in the horizontal direction are different within the range less than 10%, the arrangement pitch length of the flat convex lens 101 a in the perpendicular direction and the pitch length of the image in the perpendicular direction of the images 103A and 104B are different within the range less than 10%, and the virtual images 104A and 104B smoothly moving with respect to the displacement of the angle θ for visually observing the object to be observed can be observed. The image display sheet 1000 is light weight and in shape of sheet, and hence, even if the object 3000 to be observed is a small member (for example, mere several cm), it can be used by bonding the image display sheet 1000 of small size (for example, several mm square), so that it can be used as a position detection reference having high space-saving performance. In addition, by using a repeatedly detachable bonding agent, the image display sheet may be constituted to be freely detachable.

Further, according to the structure mentioned above, although the camera position is detected by the two virtual images 104A and 104B having different performance moving in the same direction as that of the camera, it may be possible to detect the camera position by the virtual image moving in the direction reverse to the same moving direction of the virtual image as the moving direction of the camera. For example, by constituting the pitch length of the image 103B is made larger than the arrangement pitch length of the flat convex lens 101 a, the virtual image 104B based on the flat convex lens 101 a and the image 103B can be observed and photographed. Herein, when the position of the camera 2000 changes (is moved) in the forward direction in the y-direction with respect to the object 3000 to be observed, the image 104B is photographed as an image moved in the reverse direction in the y-direction is photographed.

FIG. 23C is a view for explaining the camera position and the photographed image, and is an explanatory view relating to the movement in the x-direction of the camera position in the case of using the image display sheet in which two virtual images of which moving directions are different from each other can be observed. The photographed images 2005 (x (−1)), 2005 (x (0)) and 2005 (x (1)) are images extracted at the image obtaining portion 2003 photographed by the camera 2000. When the camera 2000 is moved in the x-direction (camera position 2000 (x (1)) and the camera position 2000 (x (−1)), the virtual image 104A (+mark) is moved in the same direction as the moving direction of the camera, and the virtual image 104B (◯mark) is moved in the direction reverse to the moving direction of the camera. The operating portion 2004 operates the relative positional relationship in the x-direction between the object 3000 to be observed and the camera 2000 based on the difference Δx between the position of the virtual image 104A and the position of the virtual image 104B, and then, detects the position of the camera 2000. The same operation will be referred to the y-direction.

FIG. 23D is a view for explaining the camera position and the photographed image, and is an explanatory view relating to the movement in the y-direction of the camera position in the case of using the image display sheet in which two virtual images of which moving directions are different from each other can be observed. When the camera 2000 is moved in the y-direction (camera position 2000 (y (1)) and the camera position 2000 (−1)), the virtual image 104A (+mark) in the photographed image 2005 (y (−1)) is moved in the same direction as the moving direction of the camera, and the virtual image 104B (◯mark) is moved in the direction reverse to the moving direction of the camera. The operating portion 2004 operates the relative positional relationship in the y-direction between the object 3000 to be observed and the camera 2000 based on the difference Δy between the position of the virtual image 104A and the position of the virtual image 104B, and then, detects the position of the camera 2000.

In comparison with the case when the virtual images 104A and 104B described above are moved in the same direction (shown in FIG. 23A and FIG. 23B), even in a case of less moving amount of the camera, since large positional differences Δx and Δy are obtained, the more accurate camera position detection can be realized.

FIG. 24A represents one example of a photographed image, and this example is the photographed image 2005 (x (−1), y (1)) in the case where the camera position is moved in an A-direction (−1 in the x-direction and 1 in the y-direction) in the case of using the image display sheet from which two virtual images of which moving directions are different from each other can be observed (FIG. 23C, FIG. 23D).

FIGS. 24B to 24E are views representing examples of photographed images in a case of using an image display sheet of another structure. For example, it is possible to detect whether or not the camera position is out of a predetermined range based on a photographed image. The pitch of the virtual image on the image display sheet is determined based on the equation (1). Because of this reason, the pitch of the virtual image can be constructed so that a plurality of virtual images based on the same images in the photographed image 2005 at the first time when the camera position takes the predetermined position. FIG. 24B is one example of the photographed image 2005 in which two virtual images are confirmed. In the case when the image 2005 of FIG. 24B is photographed, it is found out that the camera position departs from the predetermined position in the y-direction. Since it can be detected instantaneously that the camera departs from the predetermined position without waiting quantitative calculation of the camera position by the operating portion 2004, it can be applicable to the improvement in high safety of a robot, not shown, to which the camera 2000 is provided.

Any kind of mark for a virtual image may be available. Hereinbefore, although the examples of the cases using two marks of the (+mark) and the (◯mark) are explained, two marks (+mark) of the virtual images such as shown in FIG. 24C may be available. In such case, one of the virtual image of (+mark) and the other of the virtual image of (+mark) are constructed to be discriminant. For example, the virtual images are constructed in a manner such that the two virtual images have different moving amounts (performance, speed) with respect to the displacement of the angle with which the object 3000 to be observed is visually confirmed, or have difference moving directions with respect to the displacement of the angle with which the object 3000 to be observed is visually confirmed. Further, these two virtual images may be constructed with different shapes (sizes) or different colors, or may be combined.

Furthermore, a reference guide may be provided to the image display sheet 1000. FIG. 24D is a plan view of the image display sheet 1000 to which a reference guide 2006 is provided. The reference guide 2006 is located on the side at which the flat convex lens 101 a of the image display sheet 1000 has the convex shape. Further, if the reference guide 2000 could be observed from the convex-shape side of the flat convex lens 101 a, the located position of the reference guide would not be specified. In the case when the reference guide 2000 itself has no strain by the action of the lens, the reference guide may be located inside or below the flat convex lens, or even if some strain exists, as long as the strain is within a predetermined allowable range, the reference guide may be located inside or below the flat convex lens. In accordance with the positional relationship between the virtual image 104A and the reference guide 2006, the camera position can be calculated.

Another example of the reference guide 2006 is shown in FIG. 24E. The reference guide 2006, may be provided as measurement guide line as shown in FIG. 24E. If one division of the measurement guide line is determined to a time when the camera position is moved in the x- (or y-) direction, a user can be instantaneously specifies the camera position based on the photographed image provided for the user without making any operation by the operating portion 2004.

Further, at the time when the image obtaining portion 2003 extracts the part of the image display sheet from the image obtained by the camera 2000, it may be made to overlap an image (reference guide image) corresponding to the reference guide and display the same on the display portion, not shown, or provide one printed by a printer, not shown, to a user. The user grasps the movement of the camera based on the provided virtual image 104A imaged on the photographed image and the reference guide 2006, or specifies quantitatively the camera position.

With the position detection system S1, although the image display sheet using the flat convex lens was explained as an example, it may be possible to use an image display sheet using a lenticular sheet as a position detection system. The specific structure of the image display sheet to be used is the structure explained with reference to the above embodiments.

FIG. 25 is a schematic view showing a position detection system S2 to which the image display sheet according to the present invention is applicable. An image display sheet 4000A using a lenticular sheet in which cylindrical lenticular lenses are arranged in the x-direction and an image display sheet 4000B using a lenticular sheet in which cylindrical lenticular lenses are arranged in the y-direction are attached to an object 3000 to be observed. The structure other than the above is the same as that of the position detection system S1, so that the explanation thereof will be omitted herein. With the image display sheet 4000A, two virtual images 104A(A) and 104B(A) having different characteristics can be observed, and the camera position in the x-direction can be operated based on the positional difference Δx between the two virtual images 104A(A) and 104B(A) observed in the image display sheet 4000A. With the image display sheet 4000B, two virtual images 104A(B) and 104B(B) having different characteristics can be observed, and the camera position in the y-direction can be operated based on the positional difference Δy between the two virtual images 104A(B) and 104B(B) observed in the image display sheet 4000A. Two virtual images 104A(A) and 104B(A) and two virtual images 104A(B) and 104B(B) observed respectively in the image display sheets 4000A and 4000B are moved with different performance (moving amount) and/or in different directions with respect to the displacement of the angle θ with which the object 3000 can be visually observed.

In the case when it is desired to detect only the relative position in the x-direction of the object 3000 to be observed and the camera 2000, only the image display sheet 4000B may be attached to the object 3000 to be observed.

According to the structures mentioned hereinabove, the position detection system S2 can use the image display sheet 4000A (image display sheet 4000B) as the image display sheet 4000A (4000B), in which a plurality of images for displaying the virtual images in coaction with the cylindrical lenses are formed on the image forming layer in a repeated manner so as to be correspond to the respective cylindrical lenses one-on-one, the arrangement pitch length of the cylindrical lenses and the pitch length of the images formed repeatedly on the image forming layer differs from each other in a range of not more than 10%, and the virtual images 104A(A) and 104B(B) smoothly moving with respect to the displacement of the angle for visually observing the object 3000 to be observed can be observed. In the case when the only one virtual image is provided for corresponding one image display sheet 4000A (4000B), the camera position will be detected based on the difference in the moving distance of the reference position of the photographed image. The reference position is, for example, the center of the image, four corners thereof, reference guide, or like. The position for providing the reference guide is not limited as long as being viewed from the side on which the convex shape of the cylindrical lens is formed.

Consequently, the respective embodiments explained by using FIGS. 1 to 25 may be combined for the structure of the image display sheet. Furthermore, although the respective embodiments shows examples in which the lenticular sheets or flat convex lens sheets contact the image forming mediums forming the image forming layers, respectively, the present invention is not limited to such examples, and it may be possible to arrange the lenticular sheet or flat convex lens sheet and the image forming medium forming the image forming layer separately by a predetermined distance. Furthermore, it may be also possible to interpose an optional medium which does not obstruct a predetermined pseudo moving image display between the lenticular sheet or flat convex lens sheet and the image forming medium forming the image forming layers.

The applicable range of the present invention is not limited to the embodiments described hereinbefore. The present invention is widely applicable to image display sheets performing the position detection by displaying the pseudo moving image. For example, the image display sheets of the present invention can be applied to the position detection of various kinds of working robots such as medical robot, industrial robot, and the like.

REFERENCE NUMERAL

-   -   100, 200, 300, 400, 500, 600, 1000, 4000A, 4000B—image display         sheet     -   1, 5, 8, 10, 61, 71—lenticular sheet     -   1 a, 5 a, 8 a, 10 a, 61 a—cylindrical lens     -   2, 8, 11, 16, 62, 102—image forming medium     -   3, 6, 9, 12, 13, 17, 19, 20, 21, 63, 103—image forming layer     -   3 a, 6 a, 6 b, 12 a, 17 a, 19 a, 19 b, 20 a, 21 b, 63 a, 103A,         103B—image (image for observing virtual image)     -   113 b—image (image for observing virtual image, image for         observing stand still virtual image)     -   13 a, 13 b—image (other image)     -   6 c, 19 c, 113 c—cutout     -   113 d—enlarged portion     -   4, 7, 18, 114, 104A, 104B, 104A(A), 104 b(A), 104A(B),         104B(B)—virtual image     -   15, 101—flat convex lens sheet     -   15 a, 101 a—flat convex lens     -   64—flat convex lens (other convex lens)     -   2000—camera,     -   2002—position detecting device     -   2005—photographed image     -   2006—reference guide 

The invention claimed is:
 1. An image display sheet, which is provided for an object to be observed for position detection and constituted by laminating a lenticular sheet composed of arrangement of a plurality of cylindrical lenses and an image forming layer, and in which an image formed on the image forming layer from a convex shape side of the cylindrical lenses of the lenticular sheet is formed to be observable as virtual image provided with movement, or movement and deformation, wherein the lenticular sheet has a predetermined thickness so that the image forming layer is positioned on a focal surface of the cylindrical lenses, a plurality of images for observing virtual images for displaying single or a plurality of the virtual image in association with the cylindrical lenses are formed repeatedly on the image forming layer so as to correspond to the cylindrical lenses respectively one-on-one, an arrangement pitch length of the cylindrical lenses and a pitch length of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 10% , the size of the image for observing the virtual image in the arrangement direction of the cylindrical lens and the image for observing the virtual image is the size obtained by reducing the size of the virtual image along the arrangement direction, the size of the image for observing the virtual image in the vertical direction to the arrangement direction is the same size as the virtual image in the vertical direction to the arrangement direction, the virtual image smoothly moving with respect to displacement of an angle at which the object is visually observed is thereby observed, and the virtual image is photographable by a camera for detecting of the position of the object.
 2. An image display sheet, which is provided for an object to be observed for position detection and constituted by laminating a flat convex lens sheet composed of arrangement of a plurality of flat convex lenses and an image forming layer, and in which an image formed on the image forming layer from a convex shape side of the flat convex lenses of the flat convex lens sheet is formed to be observable as virtual image provided with movement, or movement and deformation, wherein the flat convex lens sheet has a predetermined thickness so that the image forming layer is positioned on a focal surface of the flat convex lenses, a plurality of images for observing virtual images for displaying single or a plurality of the virtual image in association with the flat convex lenses are formed repeatedly on the image forming layer so as to correspond to the flat convex lenses respectively one-on-one, an arrangement pitch length in a horizontal direction of the flat convex lenses and a pitch length in a horizontal direction of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 5%, and an arrangement pitch length in a vertical direction of the flat convex lenses and a pitch length in a vertical direction of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 5%, the virtual image smoothly moving with respect to displacement of an angle at which the object is visually observed is thereby observed, the image display sheet is further provided with a reference guide that is observable from a side having convex shape of the flat convex lens, and the reference guide indicates a reference position for detecting the position of the object, and the reference guide is photographable with the virtual image by a camera for detecting of the position of the object.
 3. The image display sheet according to claim 1, wherein the image display sheet is provided with a reference guide that is observable from a side having convex shape of the cylindrical lens.
 4. The image display sheet according to claim 1, wherein a plurality, not less than two kinds, of images for observing the virtual images having different pitch lengths are formed on the image forming layer repeatedly substantially one-on-one with respect to the cylindrical lenses, and a plurality of virtual images having at least one characteristic of different moving amount or different moving direction with respect to the displacement of an angle at which the object is visually observable is observable.
 5. The image display sheet according to claim 1 wherein a plurality, not less than two kinds, of images for observing the virtual images having different shapes or colors are formed on the image forming layer repeatedly substantially one-on-one with respect to the cylindrical lenses, and a plurality of virtual images having at least one characteristic of different shape and different color is observable.
 6. The image display sheet according to claim 2, wherein a plurality, not less than two kinds, of images for observing the virtual images having different pitch lengths are formed on the image forming layer repeatedly substantially one-on-one with respect to the flat convex lenses, and a plurality of virtual images having at least one characteristic of different moving amount or different moving direction with respect to the displacement of an angle at which the object is visually observable is observable.
 7. The image display sheet according to claim 2 wherein a plurality, not less than two kinds, of images for observing the virtual images having different shapes or colors are formed on the image forming layer repeatedly substantially one-on-one with respect to the flat convex lenses, and a plurality of virtual images having at least one characteristic of different shape.
 8. Position detection method using image display sheet that is provided for an object to be observed for position detection and constituted by laminating a lenticular sheet composed of arrangement of a plurality of cylindrical lenses and an image forming layer, and in which an image formed on the image forming layer from a convex shape side of the cylindrical lenses of the lenticular sheet is formed to be observable as virtual image provided with movement, or movement and deformation, the lenticular sheet has a predetermined thickness so that the image forming layer is positioned on a focal surface of the cylindrical lenses, a plurality of images for observing virtual images for displaying single or a plurality of the virtual image in association with the cylindrical lenses are formed repeatedly on the image forming layer so as to correspond to the cylindrical lenses respectively one-on-one, an arrangement pitch length of the cylindrical lenses and a pitch length of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 10% , the size of the image for observing the virtual image in the arrangement direction of the cylindrical lens and the image for observing the virtual image is the size obtained by reducing the size of the virtual image along the arrangement direction, the size of the image for observing the virtual image in the vertical direction to the arrangement direction is the same size as the virtual image in the vertical direction to the arrangement direction, comprising the steps of : photographing the image display sheet where the virtual image which is smoothly moving with respect to displacement of an angle at which the object is visually observed is thereby observed by a camera, and operating a relative positional relationship between the object and the camera based on a photographed image by the camera.
 9. Position detection method using image display sheet that is provided for an object to be observed for position detection and constituted by laminating a flat convex lens sheet composed of arrangement of a plurality of flat convex lenses and an image forming layer, and in which an image formed on the image forming layer from a convex shape side of the flat convex lenses of the flat convex lens sheet is formed to be observable as virtual image provided with movement, or movement and deformation, the flat convex lens sheet has a predetermined thickness so that the image forming layer is positioned on a focal surface of the flat convex lenses, a plurality of images for observing virtual images for displaying single or a plurality of the virtual image in association with the flat convex lenses are formed repeatedly on the image forming layer so as to correspond to the flat convex lenses respectively one-on-one, an arrangement pitch length in a horizontal direction of the flat convex lenses and a pitch length in a horizontal direction of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 5%, and an arrangement pitch length in a vertical direction of the flat convex lenses and a pitch length in a vertical direction of the image for observing virtual image formed repeatedly on the image forming layer differs in a range of not more than 5%, the image display sheet is further provided with a reference guide that is observable from a side having convex shape of the flat convex lens, comprising the steps of : photographing the image display sheet where the virtual image which is smoothly moving with respect to displacement of an angle at which the object is visually observed is thereby observed by a camera, and operating a relative positional relationship between the object and the camera based on a photographed image by the camera. 